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A294444 Number of distinct numbers appearing as denominators in row n of Kepler's triangle A294442. 2
1, 1, 1, 2, 3, 6, 10, 16, 29, 51, 83, 148, 246, 402, 650, 1084, 1740, 2803, 4458 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

It would be nice to have a formula or recurrence.

LINKS

Table of n, a(n) for n=0..18.

EXAMPLE

Row 4 of A294442 contains eight fractions,

1/5, 4/5, 3/7, 4/7, 2/7, 2/7, 3/8, 5/8.

There are three distinct denominators, so a(4) = 3.

MAPLE

# S[n] is the list of fractions, written as pairs [i, j], in row n of Kepler's triangle; nc is the number of distinct numerators, and dc the number of distinct denominators

S[0]:=[[1, 1]]; S[1]:=[[1, 2]];

nc:=[1, 1]; dc:=[1, 1];

for n from 2 to 18 do

S[n]:=[];

for k from 1 to nops(S[n-1]) do

t1:=S[n-1][k];

a:=[t1[1], t1[1]+t1[2]];

b:=[t1[2], t1[1]+t1[2]];

S[n]:=[op(S[n]), a, b];

od:

listn:={};

for k from 1 to nops(S[n]) do listn:={op(listn), S[n][k][1]}; od:

c:=nops(listn);  nc:=[op(nc), c];

listd:={};

for k from 1 to nops(S[n]) do listd:={op(listd), S[n][k][2]}; od:

c:=nops(listd);  dc:=[op(dc), c];

od:

nc; # A294443

dc; # A294444

CROSSREFS

Cf. A294442, A294443.

See A293160 for a similar sequence related to the Stern-Brocot triangle A002487.

Sequence in context: A034419 A201864 A198200 * A066895 A105075 A140669

Adjacent sequences:  A294441 A294442 A294443 * A294445 A294446 A294447

KEYWORD

nonn,more

AUTHOR

N. J. A. Sloane, Nov 20 2017

STATUS

approved

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Last modified September 18 07:39 EDT 2020. Contains 337166 sequences. (Running on oeis4.)